On Monday it issued its first ever red alerts for "very dangerous" rain in the area.
The DMI has been warning for several years that climate change is increasing torrential downpours in the Scandinavian country.
No flooding or major damage has been reported so far.
Some villages in the southeast registered more than 90 millimetres (3.5 inches) of rain in just 24 hours, an increase of more than 36 percent on the average of around 66 millimetres for the whole month of July, the DMI said.
"This is the first time we have issued alerts of this type since we began issuing warnings in 2000," DMI meteorologist Henning Gissello told AFP.
The red alert for rain in the southeast covers the period from Monday afternoon to Tuesday evening.
"We have a frontal zone over Denmark, which is producing a lot of precipitation. And the fact that it's not moving very much means that some locations get a lot," Gissello explained.
In built-up areas, the heaviest downpour was recorded in the city of Nykobing Falster (86.3 mm).
That compared to a nationwide average for the same 24-hour period of just 22 mm, the DMI said.
Gissello said that warning the authorities in advance had helped them take action and prevent major damage.
But he cautioned that the rains would continue throughout Tuesday and flooding could still occur.
"The flooding from this is more or less delayed, so we haven't seen the total effect of this yet," he said.
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